Subdividing a digital dentition model

ABSTRACT

A computer or other digital circuitry is used to assist in the creation of a digital model of an individual component, such as a tooth or gum tissue, in a patient&#39;s dentition. The computer receives a data set that forms a three-dimensional (3D) representation of the patient&#39;s dentition, applies a test to the data set to identify data elements that represent portions of the individual component, and creates a digital model of the individual component based upon the identified data elements. Many implementations require the computer to identify data elements representing a 2D cross-section of the dentition lying in a 2D plane that is roughly parallel to or roughly perpendicular to the dentition&#39;s occlusal plane. The computer analyzes the 2D cross-section to identify dentition features that represent boundaries between individual dentition components.

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] The present application is a continuation of U.S. applicationSer. No. 09/264,547 (Attorney Docket No. 018563-006000/AT00109), filedMar. 8, 1999, which was a continuation-in-part of U.S. application Ser.No. 09/169,276 (Attorney Docket No. 018563-004800/AT-00105), filed onOct. 8, 1998, (now abandoned), and entitled “Computer AutomatedDevelopment of an Orthodontic Treatment Plan and Appliance,” whichclaims priority from PCT Application No. US98/12681, filed on Jun. 19,1998, and entitled “Method and System for Incrementally Moving Teeth”(Attorney Docket No. 18563-000120PC/AT-00003PC), which claims priorityfrom U.S. application Ser. No. 08/947,080 (Attorney Docket No.18563-000110US/AT-00002), filed on Oct. 8, 1997 (now U.S. Pat. No.5,975,893), which claims priority from U.S. Provisional No. 60/050,342(Attorney Docket No. 018563-000100US/AT-000100US), filed on Jun. 20,1997, all of which are incorporated by reference into this application.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The invention relates generally to the fields of dentistry andorthodontics and, more particularly, to subdividing a digital model of apatient's dentition.

[0004] Two-dimensional (2D) and three-dimensional (3D) digital imagetechnology has recently been tapped as a tool to assist in dental andorthodontic treatment. Many treatment providers use some form of digitalimage technology to study the dentitions of patients. U.S. patentapplication Ser. No. 09/169,276, incorporated by reference above,describes the use of 2D and 3D image data in forming a digital model ofa patient's dentition, including models of individual dentitioncomponents. Such models are useful, among other things, in developing anorthodontic treatment plan for the patient, as well as in creating oneor more orthodontic appliances to implement the treatment plan.

BRIEF SUMMARY OF THE INVENTION

[0005] The inventors have developed several computer automatedtechniques for subdividing, or segmenting, a digital dentition modelinto models of individual dentition components. These dentitioncomponents include, but are not limited to, tooth crowns, tooth roots,and gingival regions. The segmentation techniques include both humanassisted and fully automated techniques. Some of the human assistedtechniques allow a human user to provide “algorithmic hints” byidentifying certain features in the digital dentition model. Theidentified features then serve as a basis for automated segmentation.Some techniques act on a volumetric 3D image model, or “voxelrepresentation,” of the dentition, and other techniques act on ageometric 3D model, or “geometric representation.”

[0006] In one aspect, a computer implementing the invention receives adata set that forms a three-dimensional (3D) representation of thepatient's dentition, applies a test to the data set to identify dataelements that represent portions of the individual component, andcreates a digital model of the individual component based upon theidentified data elements. Some implementations require the computer toidentify data elements that form one or more 2D cross-sections of thedentition in one or more 2D planes intersecting the dentition. In manyof these embodiments, these 2D planes are roughly parallel to thedentition's occlusal plane. The computer analyzes the features of the 2Dcross-sections to identify data elements that correspond to theindividual component to be modeled. For example, one technique requiresthe computer to identify cusps in the 2D cross-sectional surface of thedentition, where the cusps represent the locations of an interproximalmargin between teeth in the dentition. One variation of this techniqueallows the computer to confine its search for cusps in one 2D plane toareas in the vicinity of cusps already identified on another 2D plane.Another variation allows the computer to link cusps on adjacent 2Dplanes to form a solid surface representing the interproximal margin.Some embodiments allow the computer to receive input from a human useridentifying the cusp locations in one or more of the 2D cross sections.

[0007] Other embodiments require the computer to identify data elementsthat represent a structural core, or skeleton, of each individualcomponent to be modeled. The computer creates the model by linking otherdata elements representing the individual component to the structuralcore.

[0008] In another aspect, a computer implementing the invention receivesa three-dimensional (3D) data set representing the patient's dentition,applies a test to identify data elements that represent an interproximalmargin between two teeth in the dentition, and applies anothercomputer-implemented test to select data elements that lie on one sideof the interproximal margin for inclusion in the digital model. Someimplementations require the computer to identify data elements that formone or more 2D cross-sections of the dentition in one or more 2D planesintersecting the dentition roughly parallel to the dentition's occlusalplane.

[0009] In another aspect, a computer implementing the invention receivesa 3D data set representing at least a portion of the patient'sdentition, including at least a portion of a tooth and gum tissuesurrounding the tooth; applies a test to identify data elements lying ona gingival boundary that occurs where the tooth and the gum tissue meet;and applies a test to the data elements lying on the boundary toidentify other data elements representing portions of the tooth.

[0010] Other embodiments and advantages are apparent from the detaileddescription and the claims below.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011]FIGS. 1A, 1B, and 2 are partial views of a dentition model asdisplayed on a computer monitor and segmented with a human operated sawtool.

[0012]FIG. 3 is a partial view of a dentition model as displayed on acomputer monitor and segmented with a human operated eraser tool.

[0013]FIG. 4 is a view of a dentition model for which a feature skeletonhas been identified.

[0014]FIGS. 5 and 6 are flow diagram for a feature skeleton analysistechnique used in segmenting a dentition model.

[0015]FIG. 7A is a horizontal 2D cross-sectional view of a dentitionmodel.

[0016]FIG. 7B is a side view of a dentition model intersected by several2D planes.

[0017]FIG. 8 is a flow diagram for a 2D slice analysis technique used insegmenting a dentition model.

[0018]FIGS. 9 and 10A through 10C each shows a group of voxels in a 2Dslice of a dentition model.

[0019]FIG. 11 is a flow chart for an automatic cusp detection techniqueused in segmenting a dentition model.

[0020]FIG. 12 is a horizontal 2D cross-section of a dentition modelillustrating a neighborhood filtered automatic cusp detection techniqueused in segmenting the dentition model.

[0021]FIG. 13 is shows two groups of voxels in a 2D slice of a dentitionmodel illustrating the neighborhood filtered automatic cusp detectiontechnique.

[0022]FIG. 14 is a flow chart for the neighborhood filtered automaticcusp detection technique.

[0023]FIG. 15 is a horizontal 2D cross-section of a dentition modelillustrating an arch curve fitting technique used in segmenting thedentition model.

[0024]FIG. 16 is a flow chart for the arch curve fitting technique.

[0025]FIG. 17 is a horizontal 2D cross-section of a dentition modelillustrating a curve creation technique for use with the arch curvefitting technique.

[0026]FIG. 18 is a flow diagram for the curve creation technique.

[0027]FIGS. 19A and 19B are a perspective view and a vertical 2Dcross-sectional view of a dentition model illustrating another techniquefor use in segmenting the dentition model.

[0028]FIGS. 20 and 21 are flow diagrams of this technique.

[0029]FIG. 22 is a vertical 2D cross-sectional view of a dentition modelillustrating a gingival margin detection technique for use in segmentingthe dentition model.

[0030]FIG. 23 shows a group of voxels in a 2D slice of a dentition modelillustrating a gingival margin detection technique.

[0031]FIG. 24 is a flow diagram for the gingival margin detectiontechnique.

DETAILED DESCRIPTION OF THE INVENTION

[0032] U.S. patent application Ser. No. 09/169,276 describes techniquesfor generating a 3D digital model of a patient's dentition, includingthe crowns and roots of the patients teeth as well as the surroundinggum tissue. One such technique involves creating a physical model of thedentition from a material such as plaster and then digitally imaging themodel with a laser scanner or a destructive scanning system. Thedescribed techniques are used to produce a volumetric 3D image model(“volume element representation” or “voxel representation”) and ageometric 3D surface model (“geometric model”) of the dentition. Thetechniques described below act on one or both of these types of 3Ddentition models. In creating a voxel representation, the physical modelis usually embedded in a potting material that contrasts sharply withthe color of the model to enhance detection of the dentition features. Awhite dentition model embedded in a black potting material provides thesharpest contrast. A wide variety of information is used to enhance the3D model, including data taken from photographic images, 2D and 3Dx-rays scans, computed tomography (CT) scans, and magnetic resonanceimaging (MRI) scans of the patient's dentition.

[0033] Some computer-implemented techniques for segmenting a 3Ddentition model into models of individual dentition components require asubstantial amount of human interaction with the computer. One suchtechnique, which is shown in FIGS. 1A, 1B, and 2, provides a graphicaluser interface with a feature that imitates a conventional saw, allowingthe user to identify components to be cut away from the dentition model100. The graphical user interface provides a rendered 3D image 100 ofthe dentition model, either at one or more static views frompredetermined positions, as shown in FIGS. 1A and 1B, or in a “full 3D”mode that allows the user to alter the viewing angle, as shown in FIG.2. The saw tool is implemented as a set of mathematical control points102, represented graphically on the rendered image 100, which define a3D cutting surface 104 that intersects the volumetric or geometricdentition model. The computer subdivides the data elements in thedentition model by performing a surface intersection operation betweenthe 3D cutting surface 104 and the dentition model. The user sets thelocations of the mathematical control points, and thus the geometry andposition of the 3D cutting surface, by manipulating the control pointsin the graphical display with an input device, such as a mouse. Thecomputer provides a visual representation 104 of the cutting surface onthe display to assist the user in fitting the surface around theindividual component to be separated. Once the intersection operation iscomplete, the computer creates a model of the individual component usingthe newly segmented data elements.

[0034] Another technique requiring substantial human interaction, shownin FIG. 3, is a graphical user interface with a tool that imitates aconventional eraser. The eraser tool allows the user to isolate anindividual dentition component by removing portions of the dentitionmodel that surround the individual component. The eraser tool isimplemented as a 3D solid 110, typically having the shape of arectangular prism, or a curved surface that matches the shape of a sidesurface of a tooth. The solid is made as small as possible, usually onlya single voxel thick, to minimize degradation of the data set. As withthe saw technique above, the graphical user interface presents the userwith a rendered 3D image 112 of the dentition model at one or morepredetermined static views or in a full 3D mode. The user identifiesportions of the dentition model for removal by manipulating a graphicalrepresentation 110 of the 3D solid with an input device. In alternativeembodiments, the computer either removes the identified portions of thedentition model as the user moves the eraser 112, or the computer waitsuntil the user stops moving the eraser and provides an instruction toremove the identified portions. The computer updates the display in realtime to show the path 114 of the eraser through the dentition model.

[0035] Other computer-implemented segmentation techniques require littleor no human interaction during the segmentation process. One suchtechnique, which is illustrated in FIG. 4, involves the application ofconventional “feature skeleton” analysis to a volumetric representationof the dentition model. This technique is particularly useful inidentifying and modeling individual teeth. In general, a computerapplying this technique identifies a core of voxels, that forms askeleton 122 for the dentition 120. The skeleton 122 roughly resemblesthe network of biological nerves within patient's teeth. The computerthen divides the skeleton 122 into branches 124, each containing voxelsthat lie entirely within one tooth. One technique for identifying thebranches is by defining a plane 126 that cuts through the skeleton 122roughly parallel to the occlusal plane of the patient's dentition(“horizontal plane”). Each branch 124 intersects the horizontal plane126 at one or more points, or clusters, that are relatively distant fromthe clusters associated with the other branches. The computer forms theindividual tooth models by linking other voxels to the appropriatebranches 124 of the skeleton.

[0036]FIG. 5 describes a particular technique for forming a skeleton inthe dentition model. The computer first identifies the voxels in thedentition model that represent the tooth surfaces (step 130). For avoxel representation that is created from a physical model embedded in asharply contrasting material, identifying the tooth surfaces is assimple as identifying the voxels at which sharp changes in image valueoccur, as described in U.S. patent application Ser. No. 09/169,276. Thecomputer then calculates, for each voxel in the model, a distancemeasure indicating the physical distance between the voxel and thenearest tooth surface (step 132). The computer identifies the voxelswith the largest distance measures and labels each of these voxels asforming a portion of the skeleton (step 134). Feature skeleton analysistechniques are described in more detail in the following publications:(1) Gagvani and Silver, “Parameter Controlled Skeletons for 3DVisualization,” Proceedings of the IEEE Visualization Conference (1997);(2) Bertrand, “A Parallel Thinning Algorithm for Medial Surfaces,”Pattern Recognition Letters, v. 16, pp. 979-986 (1995); (3) Mukherjee,Chatteiji, and Das, “Thinning of 3-D Images Using the Safe PointThinning Algorithm (SPTA),” Pattern Recognition Letters, v. 10, pp.167-173 (1989); (4) Niblack, Gibbons, and Capson, “Generating Skeletonsand Centerlines from the Distance Transform,” CVGIP: Graphical Modelsand Image Processing, v. 54, n. 5, pp. 420-437 (1992).

[0037] Once a skeleton has been identified, the computer uses theskeleton to divide the dentition model into 3D models of the individualteeth. FIG. 6 shows one technique for doing so. The computer firstidentifies those portions of the skeleton that are associated with eachindividual tooth. To do so, the computer defines a plane that is roughlyparallel to the dentition's occlusal surface and that intersects theskeleton near its base (step 136). The computer then identifies pointsat which the plane and the skeleton intersect by identifying each voxelthat lies on both the skeleton and the plane (step 138). In general, asingle tooth includes all of the voxels that lie in a particular branchof the skeleton; and because the plane intersects the skeleton near itsbase, voxels that lie together in a branch of the skeleton usuallycluster together on the intersecting plane. The computer is able tolocate the branches by identifying voxels on the skeleton that liewithin a particular distance of each other on the intersecting plane(step 140). The computer then identifies and labels all voxels on theskeleton that belong to each branch (step 142).

[0038] Once the branches are identified, the computer links other voxelsin the model to the branches. The computer begins by identifying areference voxel in each branch of the skeleton (step 144). For eachreference voxel, the computer selects an adjacent voxel that does notlie on the skeleton (step 146). The computer then processes the selectedvoxel, determining whether the voxel lies outside of the dentition,i.e., whether the associated image value is above or below a particularthreshold value (step 148); determining whether the voxel already islabeled as belonging to another tooth (step 150); and determiningwhether the voxel's distance measure is greater than the distancemeasure of the reference voxel (step 152). If none of these conditionsis true, the computer labels the selected voxel as belonging to the sametooth as the reference voxel (step 154). The computer then repeats thistest for all other voxels adjacent to the reference voxel (step 156).Upon testing all adjacent voxels, the computer selects one of theadjacent voxels as a new reference point, provided that the adjacentvoxel is labeled as belonging to the same tooth, and then repeats thetest above for each untested voxel that is adjacent to the new referencepoint. This process continues until all voxels in the dentition havebeen tested.

[0039]FIGS. 7A and 7B illustrate another technique for identifying andsegmenting individual teeth in the dentition model. This technique,called “2D slice analysis,” involves dividing the voxel representationof the dentition model into a series of parallel 2D planes 160, orslices, that are each one voxel thick and that are roughly parallel tothe dentition's occlusal plane. Each of the 2D slices 160 includes a 2Dcross-section 162 of the dentition, the surface 164 of which representsthe lingual and buccal surfaces of the patient's teeth and/or gums. Thecomputer inspects the cross-section 162 in each 2D slice 160 to identifyvoxels that approximate the locations of the interproximal margins 166between the teeth. These voxels lie at the tips of cusps 165 in the 2Dcross-sectional surface 164. The computer then uses the identifiedvoxels to create 3D surfaces 168 intersecting the dentition model atthese locations. The computer segments the dentition model along theseintersecting surfaces 168 to create individual tooth models.

[0040]FIG. 8 describes a particular implementation of the 2D sliceanalysis technique. The computer begins by identifying the voxels thatform each of the 2D slices (step 170). The computer then identifies, foreach 2D slice, the voxels that represent the buccal and lingual surfacesof the patient's teeth and gums (step 172) and defines a curve thatincludes all of these voxels (step 174). This curve represents thesurface 164 of the 2D cross-section 162.

[0041] The computer then calculates the rate of curvature (i.e., thederivative of the radius of curvature) at each voxel on the 2Dcross-sectional surface 164 (step 176) and identifies all of the voxelsat which local maxima in the rate of curvature occur (step 178). Eachvoxel at which a local maximum occurs represents a “cusp” in the 2Dcross-sectional surface 164 and roughly coincides with an interproximalmargin between teeth. In each 2D slice, the computer identifies pairs ofthese cusp voxels that correspond to the same interproximal margin (step180), and the computer labels each pair to identify the interproximalmargin with which it is associated (step 182). The computer thenidentifies the voxel pairs on all of the 2D slices that represent thesame interproximal margins (step 184). For each interproximal margin,the computer fits a 3D surface 168 approximating the geometry of theinterproximal margin among the associated voxel pairs (step 186).

[0042]FIG. 9 illustrates one technique for creating the 3D surfaces thatapproximate the interproximal margins. For each pair of cusp voxels 190a-b in a 2D slice that are associated with a particular interproximalregion, the computer creates a line segment 192 bounded by these cuspvoxels 190 a-b. The computer changes the colors of the voxels in theline segment, including the cusp voxels 190 a-b that bound the segment,to contrast with the other voxels in the 2D slice. The computer createsline segments in this manner in each successive 2D slice, forming 3Dsurfaces that represent the interproximal regions. All of the voxelsthat lie between adjacent ones of these 3D surfaces represent anindividual tooth.

[0043]FIGS. 10A through 10C illustrate a refinement of the techniqueshown in FIG. 9. The refined technique involves the projection of a linesegment 200 from one slice onto a line segment 206 on the nextsuccessive slice to form, for the associated interproximal margin, a 2Darea bounded by the cusp voxels 202 a-b, 204 a-b of the line segments200, 206. If the line segments 200, 206 are oriented such that any voxelon one segment 200 is not adjacent to a voxel on the other segment 206,as shown in FIG. 10A, then the resulting 3D surface is discontinuous,leaving unwanted “islands” of white voxels 208, 210.

[0044] The computer eliminates these discontinuities by creating two newline segments 212, 214, each of which is bounded by one cusp voxel 202a-b, 204 a-b from each original line segment 200, 206, as shown in FIG.10B. The computer then eliminates the islands between the new linesegments 212, 214 by changing the colors of all voxels between the newline segments 212, 214, as shown in FIG. 10C.

[0045] Automated segmentation is enhanced through a technique known as“seed cusp detection.” The term “seed cusp” refers to a location atwhich an interproximal margin meets the patient's gum tissue. In avolumetric representation of the patient's dentition, a seed cusp for aparticular interproximal margin is found at the cusp voxel that liesclosest to the gumline. By applying the seed cusp detection technique ofthe 2D slice analysis, the computer is able to identify all of the seedcusp voxels in the 3D model automatically.

[0046]FIG. 11 shows a particular implementation of the seed cuspdetection technique, in which the computer detects the seed cusps byidentifying each 2D slice in which the rate of curvature of a cusp firstfalls below a predetermined threshold value. The computer begins byselecting a 2D slice that intersects all of the teeth in the arch (step220). The computer attempts to select a slice that is near the gingivalregions but that does not include any voxels representing gingivaltissue. The computer then identifies all of the cusp voxels in the 2Dslice (step 222). If the rate of curvature of the 2D cross-section atany of the cusp voxels is less than a predetermined threshold value, thecomputer labels that voxel as a seed cusp (step 224). The computer thenselects the next 2D slice, which is one voxel layer closer to thegingival region (step 226), and identifies all of the cusp voxels thatare not associated with a cusp for which the computer has alreadyidentified a seed cusp (step 228). If the rate of curvature of the 2Dcross-section is less than the predetermined threshold value at any ofthese cusp voxels, the computer labels the voxel as a seed cusp (step230) and proceeds to the next 2D slice. The computer continues in thismanner until a seed cusp voxel has been identified for each cuspassociated with an interproximal margin (step 232).

[0047]FIGS. 12, 13, and 14 illustrate a technique, known as“neighborhood-filtered cusp detection,” by which the computer focusesits search for cusps on one 2D slice to neighborhoods 244, 246 of voxelsdefined by a pair of previously detected cusp voxels 240, 242 on another2D slice. Upon detecting a pair of cusp voxels 240, 242 in a 2D slice atlevel N (step 250), the computer defines one or more neighborhoods 244,246 that include a predetermined number of voxels surrounding the pair(step 252). The computer then projects the neighborhoods onto the next2D slice at level N+1 by identifying the voxels on the next slice thatare immediately adjacent the voxels in the neighborhoods on the originalslice (step 254). The neighborhoods are made large enough to ensure thatthey include the cusp voxels on the N+1 slice. In the example of FIG.13, each cusp voxel 240, 242 lies at the center of a neighborhood 244,246 of twenty-five voxels arranged in a 5×5 square.

[0048] In searching for the cusp voxels on the N+1 slice, the computertests the image values for all voxels in the projected neighborhoods toidentify those associated with the background image and those associatedwith the dentition (step 256). In the illustrated example, voxels in thebackground are black and voxels in the dentition are white. The computeridentifies the cusp voxels on the N+1 slice by locating the pair ofblack voxels in the two neighborhoods that lie closest together (step258). The computer then repeats this process for all remaining slices(step 259).

[0049]FIGS. 15 and 16 illustrate another technique, known as “arch curvefitting,” for identifying interproximal margins between teeth in thedentition. The arch curve fitting technique, which also applies to 2Dcross-sectional slices of the dentition, involves the creation of acurve 260 that fits among the voxels on the 2D cross-sectional surface262 of the dentition arch 264. A series of closely-spaced line segments268, each bounded by the cross-sectional surface 268, are formed alongthe curve 260, roughly perpendicular to the curve 260, throughout the 2Dcross-section 264. In general, the shortest of these line segments 268lie on or near the interproximal margins; thus computer identifies thecusps that define the interproximal margins by determining the relativelengths of the line segments 268.

[0050] When applying the arch curve fitting technique, the computerbegins by selecting a 2D slice (step 270) and identifying the voxelsassociated with the surface 262 of the cross-sectional arch 264 (step272). The computer then defines a curve 260 that fits among the voxelson the surface 262 of the arch (step 274). The computer creates thecurve using any of a variety of techniques, a few of which are discussedbelow. The computer then creates a series of line segments that areroughly perpendicular to the curve and are bounded by thecross-sectional surface 262 (step 276). The line segments areapproximately evenly spaced with a spacing distance that depends uponthe required resolution and the acceptable computing time. Greaterresolution leads to more line segments and thus greater computing time.In general, a spacing on the order of 0.4 mm is sufficient in theinitial pass of the arch curve fitting technique.

[0051] The computer calculates the length of each line segment (step278) and then identifies those line segments that form local minima inlength (step 280). These line segments roughly approximate the locationsof the interproximal boundaries, and the computer labels the voxels thatbound these segments as cusp voxels (step 282). The computer repeatsthis process for each of the 2D slices (step 284) and then uses the cuspvoxels to define 3D cutting surfaces that approximate the interproximalmargins.

[0052] In some implementations, the computer refines the arch cuspdetermination by creating several additional sets of line segments, eachcentered around the arch cusps identified on the first pass. The linesegments are spaced more narrowly on this pass to provide greaterresolution in identifying the actual positions of the arch cusps.

[0053] The computer uses any of a variety of curve fitting techniques tocreate the curve through the arch. One technique involves the creationof a catenary curve with endpoints lying at the two ends 265, 267 (FIG.15) of the arch. The catenary curve is defined by the equationy=a+b·cosh(cx), and the computer fits the curve to the arch by selectingappropriate values for the constants a, b, and c. Another techniqueinvolves the creation of two curves, one fitted among voxels lying onthe front surface 271 of the arch, and the other fitted among voxels onthe rear surface 273. A third curve, which guides the placement of theline segments above, passes through the middle of the area lying betweenthe first two curves.

[0054]FIGS. 17 and 18 illustrate another technique for constructing acurve through the arch. This technique involves the creation of a seriesof initial line segments through the arch 264 and the subsequentformation of a curve 290 fitted among the midpoints of these linesegments This curve 290 serves as the arch curve in the arch curvefitting technique described above.

[0055] In applying this technique, the computer first locates an end 265of the arch (step 300) and creates a line segment 291 that passesthrough the arch 264 near this end 265 (step 301). The line segment 291is bounded by voxels 292 a-b lying on the surface of the arch. Thecomputer then determines the midpoint 293 of the line segment 291 (step302), selects a voxel 294 located particular distance from the midpoint293 (step 304), and creates a second line segment 295 that is parallelto the initial line segment 291 and that includes the selected voxel 294(step 306). The computer then calculates the midpoint 296 of the secondsegment 295 (step 308) and rotates the second segment 295 to theorientation 295′ that gives the segment its minimum possible length(step 309). In some cases, the computer limits the second segment 295 toa predetermined amount of rotation (e.g., ±10°).

[0056] The computer then selects a voxel 297 located a particulardistance from the midpoint 296 of the second segment 295 (step 310) andcreates a third line segment 298 that is parallel to the second linesegment 295 and that includes the selected voxel 297 (step 312). Thecomputer calculates the midpoint 299 of the third segment 298 (step 314)and rotates the segment 298 to the orientation 298′ that gives thesegment its shortest possible length (step 316). The computer continuesadding line segments in this manner until the other end of thecross-sectional arch is reached (step 318). The computer then creates acurve that fits among the midpoints of the line segments (step 320) anduses this curve in applying the arch fitting technique described above.

[0057]FIGS. 19A, 19B and 20 illustrate an alternative technique forcreating 3D surfaces that approximate the geometries and locations ofthe interproximal margins in the patient's dentition. This techniqueinvolves the creation of 2D planes that intersect the 3D dentition modelat locations that approximate the interproximal margins. In general, thecomputer defines a series of planes, beginning with an initial plane 330at one end 331 of the arch 332, that are roughly perpendicular to theocclusal plane of the dentition model (“vertical” planes). Each planeintersects the dentition model to form a 2D cross-section 334. If theplanes are spaced sufficiently close to each other, the planes with thesmallest cross-sectional areas approximate the locations of theinterproximal margins in the dentition. The computer locates theinterproximal regions more precisely by rotating each plane about twoorthogonal axes 336, 338 until the plane reaches the orientation thatyields the smallest possible cross-sectional area.

[0058] In one implementation of this technique, the computer firstidentifies one end of the arch in the dentition model (step 340). Thecomputer then creates a vertical plane 330 through the arch near thisend (step 342) and identifies the centerpoint 331 of the plane 330 (step344). The computer then selects a voxel located a predetermined distancefrom the centerpoint (step 345) and creates a second plane 333 that isparallel to the initial plane and that includes the selected voxel (step346). The computer calculates the midpoint of the second plane (step348) and rotates the second plane about two orthogonal axes thatintersect at the midpoint (step 350). The computer stops rotating theplane upon finding the orientation that yields the minimumcross-sectional area. In some cases, the computer limits the plane to apredetermined amount of rotation (e.g., ±10° about each axis). Thecomputer then selects a voxel located a particular distance from themidpoint of the second plane (step 352) and creates a third plane thatis parallel to the second plane and that includes the selected voxel(step 354). The computer calculates the midpoint of the third plane(step 356) and rotates the plane to the orientation that yields thesmallest possible cross-sectional area (step 357). The computercontinues adding and rotating planes in this manner until the other endof the arch is reached (step 358). The computer identifies the planes atwhich local minima in cross-sectional area occur and labels these planesas “interproximal planes,” which approximate the locations of theinterproximal margins (step 360).

[0059] One variation of this technique, described in FIG. 21, allows thecomputer to refine its identification of interproximal planes bycreating additional, more closely positioned planes in areas around theplanes labeled as interproximal. The computer first creates a curve thatfits among the midpoints of the planes labeled as interproximal planes(step 372) and then creates a set of additional planes along this curve(step 374). The additional planes are not evenly spaced along the curve,but rather are concentrated around the interproximal margins. The planesin each interproximal area are spaced very closely (e.g., 0.05 mm fromeach other). The computer rotates each of the newly constructed planesabout two orthogonal axes until the plane reaches its minimumcross-sectional area (step 376). The computer then selects the plane ineach cluster with the smallest cross-sectional area as the plane thatmost closely approximates the interproximal margin (step 378).

[0060]FIGS. 22, 23, and 24 illustrate a technique for identifying thegingival margin that defines the boundary between tooth and gum in thepatient's dentition. This technique involves the creation of a series ofhorizontal 2D planes 380, or slices, that intersect the dentition modelroughly perpendicular to the occlusal plane (see FIG. 19A). Thecross-sectional surface 382 of the dentition model in each of theseplanes 380 includes cusps 384, 386 that represent the gingival margin.The computer identifies the gingival margin by applying one or more ofthe cusp detection techniques described above.

[0061] One technique is very similar to the neighborhood filtered cuspdetection technique described above, in that voxel neighborhoods 388,390 are defined on one of the 2D planes to focus the computer's searchfor cusps on an adjacent 2D plane. Upon detecting a pair of cusps 384,386 on one 2D plane (step 400), the computer defines one or moreneighborhoods 388, 390 to include a predetermined number of voxelssurrounding the pair (step 402). The computer projects the neighborhoodsonto an adjacent 2D plane by identifying the voxels on the adjacentplane that correspond to the voxels in the neighborhoods 388, 390 on theoriginal plane (step 404). The computer then identifies the pair ofblack voxels that lie closest together in the two neighborhoods on theadjacent plane, labeling these voxels as lying in the cusp (step 406).The computer repeats this process for all remaining planes (step 408).

[0062] Many of these automated segmentation techniques are even moreuseful and efficient when used in conjunction with human-assistedtechniques. For example, techniques that rely on the identification ofthe interproximal or gingival margins function more quickly andeffectively when a human user first highlights the interproximal orgingival cusps in a graphical representation of the dentition model. Onetechnique for receiving this type of information from the user is bydisplaying a 2D or 3D representation and allowing the user to highlightindividual voxels in the display. Another technique allows the user toscroll through a series of 2D cross-sectional slices, identifying thosevoxels that represent key features such as interproximal or gingivalcusps. Some of these techniques rely on user interface tools such ascursors and bounding-box markers.

[0063] In many instances, the computer creates proposals for segmentingthe dentition model and then allows the user to select the bestalternative. For example, one version of the arch curve fittingtechnique requires the computer to create a candidate catenary or splinecurve, which the user is allowed to modify by manipulating themathematical control parameters. Other techniques involve displayingseveral surfaces that are candidate cutting surfaces and allowing theuser to select the appropriate surfaces.

[0064] Some implementations of the invention are realized in digitalelectronic circuitry, such as an application specific integrated circuit(ASIC); others are realized in computer hardware, firmware, andsoftware, or in combinations of digital circuitry and computercomponents. The invention is usually embodied, at least in part, as acomputer program tangibly stored in a machine-readable storage devicefor execution by a computer processor. In these situations, methodsembodying the invention are performed when the processor executesinstructions organized into program modules, operating on input data andgenerating output. Suitable processors include general and specialpurpose microprocessors, which generally receive instructions and datafrom read-only memory and/or random access memory devices. Storagedevices that are suitable for tangibly embodying computer programinstructions include all forms of non-volatile memory, includingsemiconductor memory devices, such as EPROM, EEPROM, and flash memorydevices; magnetic disks such as internal hard disks and removable disks;magneto-optical disks; and CD-ROM.

[0065] The invention has been described in terms of particularembodiments. Other embodiments are within the scope of the followingclaims.

What is claimed is:
 1. A computer-implemented method for use in creatinga digital model of an individual component of a patient's dentition, themethod comprising: (a) receiving a data set that forms athree-dimensional (3D) representation of the patient's dentition; (b)applying a computer-implemented test to the data set to identify dataelements that represent portions of an individual component of thepatient's dentition; and (c) creating a digital model of the individualcomponent based upon the identified data elements.
 2. The method ofclaim 1, wherein the data set includes data taken from at least one ofthe following sources: two-dimensional (2D) x-ray data andthree-dimensional (3D) x-ray data.
 3. The method of claim 1, wherein thedata set includes data taken from at least one of the following sources:computed tomography (CT) scan data and magnetic resonance imaging (MRI)scan data.
 4. The method of claim 1, wherein the data set includes datataken from a photographic image of the patient's dentition.
 5. Themethod of claim 1, wherein some of the data is obtained by imaging aphysical model of the patient's teeth.
 6. The method of claim 1, whereinsome of the data is obtained by imaging the patient's teeth directly. 7.The method of claim 1, wherein the data set forms a 3D volumetricrepresentation of the patient's dentition.
 8. The method of claim 1,wherein the data set includes geometric surface data that forms a 3Dgeometric surface model of the patient's dentition.
 9. The method ofclaim 1, wherein the individual component is an individual tooth in thepatient's dentition.
 10. The method of claim 1, wherein the individualcomponent includes gum tissue found in the patient's dentition.
 11. Themethod of claim 1, wherein applying the computer-implemented testincludes receiving information input by a human user to identify aboundary of the individual component to be modeled.
 12. The method ofclaim 11, wherein receiving information includes receiving position datafrom a computer-implemented tool through which the human user identifiesthe boundary in a graphical representation of the patient's dentition.13. The method of claim 12, wherein the computer-implemented tool is asaw tool that allows the user to identify the boundary by defining acurve in the graphical representation that separates the data elementsassociated with the individual component from other elements of the dataset.
 14. The method of claim 12, wherein the computer-implemented toolis an eraser tool that allows the user to identify the boundary byerasing a portion of the graphical representation representing theboundary.
 15. The method of claim 1, wherein receiving the data,applying the computer-implemented test, and creating the electronicmodel all are carried out by a computer without human intervention. 16.The method of claim 1, wherein applying the computer-implemented testincludes automatically applying a rule to identify a boundary of theindividual component to be modeled.
 17. The method of claim 16, whereinthe boundary includes a surface of a tooth.
 18. The method of claim 16,wherein the boundary includes a gingival margin.
 19. The method of claim1, wherein applying the computer-implemented test includes identifyingelements of the data set that represent a structural core of theindividual component to be modeled and labeling those data elements asbelonging to the individual component.
 20. The method of claim 19,further comprising applying another computer-implemented test toidentify elements of the data set that represent a structural core ofanother individual component of the dentition and labeling those dataelements as belonging to the other individual component.
 21. The methodof claim 20, wherein applying the computer-implemented tests includesapplying tests to link other elements of the data set to thoserepresenting the structural cores of the individual components andlabeling the linked elements as belonging to the individual componentsto which they are linked.
 22. The method of claim 21, wherein applyingthe tests to link other data elements to the structural cores of theindividual components includes determining whether a data elementalready is labeled as belonging to one of the individual components. 23.The method of claim 1, wherein applying the computer implemented testincludes identifying an initial 2D cross-section of the individualcomponent having continuous latitudinal width, a relative minimum valueof which occurs at an end of the initial cross-section.
 24. The methodof claim 23, wherein applying the computer-implemented test includesisolating portions of the data corresponding to the initial 2Dcross-section of the individual component to be modeled.
 25. The methodof claim 24, wherein the received data includes 3D image data obtainedby imaging the individual component volumetrically, and whereinisolating portions of the data corresponding to the initial 2Dcross-section includes isolating elements of the 3D image datarepresenting the initial 2D cross-section.
 26. The method of claim 23,wherein applying the computer-implemented test includes applying a testto identify the end of the initial cross-section at which the relativeminimum value of the latitudinal width occurs.
 27. The method of claim26, wherein applying the test to identify the end of the initialcross-section includes: (a) establishing line segments within theinitial cross-section, each of which is bounded at each end by anendpoint lying on a surface of the individual component, and each ofwhich is roughly perpendicular to a latitudinal axis of the individualcomponent; (b) calculating a length for each line segment; and (c)identifying elements of the data set that correspond to the endpoints ofthe line segment with the shortest length.
 28. The method of claim 27,wherein applying the computer-implemented test also includes: (a)isolating portions of the data set corresponding to other 2Dcross-sectional of the individual component, all lying in planesparallel to the initial 2D cross-sectional; (b) for each of the othercross-sections, identifying data elements that correspond to endpointsof a line segment representing an end of the cross-section; and (c)defining a solid surface that contains all of the identified dataelements.
 29. The method of claim 28, further comprising labeling thesolid surface as representing a surface of the individual component tobe modeled.
 30. The method of claim 28, further comprising using thedata elements identified in the initial cross-section as guides foridentifying the data elements in the other cross-sections.
 31. Themethod of claim 26, wherein applying the test to identify the end of theinitial cross-section includes first creating an initial curve that isroughly perpendicular to the latitudinal axis of the individualcomponent and that is fitted between the surfaces of the 2Dcross-section on which the endpoints of the line segments will lie. 32.The method of claim 31, wherein establishing the line segments includesfirst establishing a set of initial line segments that are roughlyperpendicular to the curve and to the latitudinal axis and that haveendpoints lying on the surfaces of the individual component.
 33. Themethod of claim 32, wherein establishing the line segments also includespivoting each initial line segment about a point at which the initialline segment intersects the curve until the initial line segment has itsshortest possible length.
 34. The method of claim 33, whereinestablishing the line segments also includes: (a) locating a midpointfor each of the initial line segments after pivoting; and (b) creating arefined curve that passes through all of the midpoints.
 35. The methodof claim 34, wherein establishing the line segments also includescreating the line segments to be perpendicular to the refined curve. 36.The method of claim 31, wherein the individual component is a tooth andthe curve is a portion of a larger curve fitted among the lingual andbuccal surfaces of all teeth in a 2D cross-section of a tooth arch inwhich the tooth lies.
 37. The method of claim 36, wherein the largercurve is a catenary.
 38. The method of claim 36, wherein the largercurve is created by manipulating mathematical control points to fit thecurve to the shape of the cross-section of the tooth arch.
 39. Themethod of claim 27, wherein establishing the line segments includesfirst establishing an initial line segment by creating a line thatintersects the initial 2D cross-section, such that the initial linesegment has endpoints that lie on surfaces of the individual component.40. The method of claim 39, wherein establishing the line segments alsoincludes establishing at least one additional line segment parallel toand spaced a predetermined distance from a previously established linesegment.
 41. The method of claim 39, wherein establishing the linesegments also includes, for each additional line segment, locating amidpoint of the additional line segment and pivoting the additional linesegment about the midpoint until the additional line segment has itsshortest possible length.
 42. The method of claim 41, whereinestablishing the line segments also includes limiting the rotation ofeach additional line segment to no more than a predetermined amount. 43.The method of claim 42, wherein the rotation of each additional linesegment is limited to no more than approximately +/−10°.
 44. The methodof claim 41, wherein establishing the line segments also includesestablishing a curve that is fitted among the midpoints of theadditional line segments.
 45. The method of claim 44, whereinestablishing the line segments includes establishing the line segmentsto be perpendicular to the curve.
 46. The method of claim 45, whereinestablishing the line segments includes locating midpoints for each ofthe line segments and pivoting each line segment about its midpointuntil the line segment has its shortest possible length.
 47. The methodof claim 23, wherein the individual component is a tooth and therelative minimum value of the initial 2D cross-section lies on aninterproximal surface of the tooth.
 48. The method of claim 47, whereinidentifying the initial 2D cross-section includes isolating elements ofthe data set that correspond to 2D cross-sections of the tooth lying inparallel planes between the roots and the occlusal surface of the tooth.49. The method of claim 48, wherein identifying the initial 2Dcross-section also includes identifying adjacent ones of the 2Dcross-sections in which the interproximal surface of the tooth isobscured by gum tissue in one of the adjacent cross-sections and is notobscured by gum tissue in the other adjacent cross-section.
 50. Themethod of claim 49, wherein identifying the initial 2D cross-sectionalso includes selecting as the initial 2D cross-section the adjacentcross-section in which the interproximal surface of the tooth is notobscured by gum tissue.
 51. The method of claim 48, wherein identifyingthe initial 2D cross-section also includes, for each of the isolatedcross-sections, establishing a contour line that outlines the shape ofthe dentition in that cross-section.
 52. The method of claim 51, whereinidentifying the initial 2D cross-section also includes applying a testto each of the isolated cross-sections to identify those cross-sectionsin which the interproximal surface of the tooth is not obscured by gumtissue.
 53. The method of claim 52, wherein applying the test includescalculating the rate of curvature of the contour line.
 54. The method ofclaim 52, wherein identifying the initial 2D cross-section includesselecting as the initial 2D cross-section the isolated cross-sectionthat lies closest to the roots of the tooth and in which theinterproximal surface of the tooth is not obscured by gum tissue. 55.The method of claim 23, wherein applying the computer-implemented testalso includes identifying two elements of the data set that defineendpoints of a line segment spanning the relative minimum width of theinitial 2D cross-section.
 56. The method of claim 55, wherein applyingthe computer-implemented test also includes defining, for each endpoint,a neighborhood containing a predetermined number of elements of the dataset near the endpoint in the initial 2D cross-section.
 57. The method ofclaim 56, wherein applying the computer-implemented test also includesidentifying an additional 2D cross-section of the individual componentin a plane parallel and adjacent to the initial 2D cross-section, wherethe additional 2D cross-section also has a continuous, latitudinal widthwith a relative minimum value occurring at one end of the cross-section.58. The method of claim 57, wherein applying the computer-implementedtest also includes identifying two elements of the data set that defineendpoints of a line segment spanning the relative minimum width of theadditional 2D cross-section by: (a) defining two neighborhoods of dataelements, each containing elements of the data set that are adjacent tothe data elements contained in the neighborhoods defined for the initial2D cross-section; and (b) identifying one data element in eachneighborhood that corresponds to one of the endpoints of the linesegment spanning the relative minimum width of the additional 2Dcross-section.
 59. The method of claim 57, further comprisingestablishing a solid surface that is fitted among line segments spanningthe relative minimum widths of the parallel 2D cross-sections.
 60. Themethod of claim 59, wherein the individual component to be modeled is atooth and the solid surface represents an interproximal surface of thetooth.
 61. The method of claim 23, further comprising receivinginformation provided by a human user that identifies elements of thedata set that correspond to the relative minimum width of the initial 2Dcross-section.
 62. The method of claim 61, further comprising displayinga graphical representation of the patient's dentition in which the useridentifies portions corresponding to the relative minimum width of thecross-section.
 63. The method of claim 62, wherein the graphicalrepresentation is three dimensional.
 64. The method of claim 62, whereinthe graphical representation includes a 2D representation of the initial2D cross-section.
 65. The method of claim 64, further comprisingreceiving the information from an input device used by the human user toidentify the relative minimum width of the initial 2D cross-section inthe graphical representation.
 66. The method of claim 64, wherein theinitial 2D cross-section is one of many 2D cross-sections displayed tothe human user.
 67. The method of claim 64, further comprising receivinginformation from the human user identifying which of the displayed 2Dcross-sections is the initial 2D cross-section.
 68. Acomputer-implemented method for use in creating a digital model of atooth in a patient's dentition, the method comprising: (a) receiving athree-dimensional (3D) data set representing the patient's dentition;(b) applying a computer-implemented test to identify data elements thatrepresent an interproximal margin between two teeth in the dentition;(c) applying another computer-implemented test to select data elementsthat lie on one side of the interproximal margin for inclusion in thedigital model.
 69. The method of claim 68, further comprising creating aset of 2D planes that intersect the dentition roughly perpendicular toan occlusal plane of the dentition, each 2D plane including dataelements that form a 2D cross-section of the dentition.
 70. The methodof claim 69, further comprising identifying the 2D plane with thesmallest cross-sectional area.
 71. The method of claim 70, furthercomprising rotating the 2D plane with the smallest cross-sectional areato at least one other orientation to form at least one other 2Dcross-section of the dentition.
 72. The method of claim 71, furthercomprising selecting the orientation that gives the rotated plane itssmallest possible cross-sectional area.
 73. The method of claim 72,further comprising identifying data elements that represent the selectedorientation of the rotated plane as lying on an interproximal margin.74. The method of claim 71, wherein the plane is rotated about twoorthogonal lines passing through its center point.
 75. The method ofclaim 70, further comprising creating a set of additional 2D planes inthe vicinity of the 2D plane with the smallest cross-sectional area. 76.The method of claim 75, further comprising identifying the plane in theset of additional planes that has the smallest cross-sectional area. 77.The method of claim 76, further comprising rotating the plane with thesmallest cross-sectional area to at least one other orientation to format least one other 2D cross-section of the dentition.
 78. The method ofclaim 77, further comprising selecting the orientation that produces the2D cross-section with the smallest possible area.
 79. The method ofclaim 69, wherein creating a set of 2D planes includes creating aninitial plane near one end of the dentition.
 80. The method of claim 79,further comprising selecting a point in the dentition that is apredetermined distance from the initial plane and creating a secondplane.
 81. The method of claim 80, wherein the second plane is roughlyparallel to the initial plane.
 82. The method of claim 80, furthercomprising rotating the second plane to at least one additionalorientation to form at least one additional 2D cross-section of thedentition.
 83. The method of claim 82, further comprising selecting theorientation that produces the 2D cross-section with the smallestcross-sectional area.
 84. The method of claim 82, further comprisingselecting a point that is a predetermined distance from the second planeand creating a third plane that includes the selected point.
 85. Themethod of claim 84, further comprising rotating the third plane to atleast one other orientation to create at least one additional 2Dcross-section of the dentition.
 86. The method of claim 84, furthercomprising creating additional planes, each including a point that is apredetermined distance from a preceding plane, until the other end ofthe dentition is reached.
 87. The method of claim 86, further comprisingidentifying at least one plane having a local minimum in cross-sectionalarea.
 88. The method of claim 86, further comprising identifying acenterpoint of the cross-section in each of the planes and creating acurve that fits among the identified centerpoints.
 89. The method ofclaim 88, further comprising creating a set of additional 2D planesalong the curve, where the curve is roughly normal to each of theadditional planes, and where each of the additional planes is roughlyperpendicular to the occlusal plane.
 90. The method of claim 89, furthercomprising identifying at least one of the additional planes that has alocal minimum in cross-sectional area.
 91. A computer-implemented methodfor use in creating a digital model of a tooth in a patient's dentition,the method comprising: (a) receiving a 3D dataset representing at leasta portion of the patient's dentition, including at least a portion of atooth and gum tissue surrounding the tooth; (b) applying a test toidentify data elements lying on a gingival boundary that occurs wherethe tooth and the gum tissue meet; and (c) applying a test to the dataelements lying on the boundary to identify other data elementsrepresenting portions of the tooth.
 92. The method of claim 91, whereinapplying the test to identify data elements on the gingival boundaryincludes creating an initial 2D plane that intersects the dentitionroughly perpendicular to an occlusal plane of the dentition and thatincludes data elements representing an initial cross-sectional surfaceof the dentition.
 93. The method of claim 91, wherein applying the testto identify data elements on the gingival boundary includes creating aseries of roughly parallel 2D planes, each intersecting the dentitionroughly perpendicular to an occlusal plane of the dentition, and eachincluding data elements that represent a cross-sectional surface of thedentition.
 94. The method of claim 93, wherein the cross-sectionalsurface in each 2D plane includes two cusps that roughly identify thelocations of the gingival boundary.